We consider the problem of resolution of singularities for differential operators defined on manifolds.

We will see that the known results of resolution of singularities for vector fields and principal ideal sheafs are particular cases of a conjectured result in this more general framework.

We will briefly expose some new techniques coming from geometric invariant theory which can be useful to tackle this conjecture. For instance, they can be used to prove a result of resolution for differential operators on surfaces.